1,720,966 research outputs found
Fast methods for the Boltzmann collision integral
No full textIn this Note we present methods for the development of fast numerical schemes for the Boltzmann collision integral. These schemes are based on a combination of a Carleman-like representation together with a suitable angular approximation. For the hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. Estimates for the errors and spectral accuracy are also given
Solving the Boltzmann equation in NlogN
No full textIn [33, 32], fast deterministic algorithms based on spectral methods were
derived for the Boltzmann collision operator for a class of interactions including the hard
spheres model in dimension three. These algorithms are implemented for the solution of
the Boltzmann equation in dimension two and three, first for homogeneous solutions, then
for general nonhomogeneous solutions. The results are compared to explicit solutions,
when available, and to Monte-Carlo methods. In particular, the computational cost and
accuracy are compared to those of Monte-Carlo methods as well as to those of previous
spectral methods. Finally, for inhomogeneous solutions, we take advantage of the great
computational efficiency of the method to show an oscillation phenomenon of the entropy
functional in the trend to equilibrium, which was suggested in [16]
Uniqueness of the non-equilibrium steady state for a 1d BGK model in kinetic theory
No full textWe continue our investigation of kinetic models of a one-dimensional gas in contact with homogeneous thermal reservoirs at different temperatures. Nonlinear collisional interactions between particles are modeled by a so-called BGK dynamics which conserves local energy and particle density. Weighting the nonlinear BGK term with a parameter alpha is an element of[0,1], and the linear interaction with the reservoirs by (1-alpha), we prove that for some alpha close enough to zero, the explicit spatially uniform non-equilibrium steady state (NESS) is unique, and there are no spatially non-uniform NESS with a spatial density rho belonging to Lp for any p>1. We also show that for all alpha is an element of[0,1], the spatially uniform NESS is dynamically stable, with small perturbation converging to zero exponentially fast
Approach to the Steady State in Kinetic Models with Thermal Reservoirs at Different Temperatures
No full textWe continue the investigation of kinetic models of a system in contact via stochastic interactions with several spatially homogeneous thermal reservoirs at different temperatures. Considering models different from those investigated in Carlen et al. (Braz J Probab Stat 29:372–386, 2015), we explicitly compute the unique spatially uniform non-equilibrium steady state (NESS) and prove that it is approached exponentially fast from any uniform initial state. This leaves open the question of whether there exist NESS that are not spatially uniform. Making a further simplification of our models, we then prove non-existence of such NESS and exponential approach to the unique spatially uniform NESS (with a computably boundable rate). The method of proof relies on refined Doeblin estimates and other probabilistic techniques, and is quite different form the analysis in Carlen et al. (Braz J Probab Stat 29:372–386, 2015) that was based on contraction mapping methods
Fast algorithms for computing the Boltzmann collision operator
No full textThe development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres model in dimension three, we are able to derive spectral methods that can be evaluated through fast algorithms. These algorithms are based on a suitable representation and approximation of the collision operator. Explicit expressions for the errors in the schemes are given and spectral accuracy is proved. Parallelization properties and adaptivity of the algorithms are also discussed.ou
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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